Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

The Pauli Exclusion Principle

The Pauli Exclusion Principle

The arrangement of electrons in the orbitals of an atom is called its electron configuration. We describe an electron configuration with a symbol that contains three pieces of information:

Work-energy Theorem

Work-energy Theorem

According to Newton’s second law of motion, the sum of all the forces acting on a particle (net force) determines the rate of change in the momentum of the particle (motion). Therefore, we should consider the work done by all forces acting on a particle, or the net work, to see its effect on the particle’s motion.
The work-energy theorem equates work done by all the forces on an object to the change in its kinetic energy. The theorem can be used to calculate work done by a force...

Internal Energy

Internal Energy

The total of all possible kinds of energy present in a substance is called the internal energy (U), sometimes symbolized as E. Suppose a system with initial internal energy, Uinitial, undergoes a change in energy (transfer of work or heat), and the final internal energy of the system is Ufinal. Change in internal energy equals the difference between Ufinal and Uinitial.

Quantifying Work

Quantifying Work

As a system undergoes a change, its internal energy can change, and energy can be transferred from the system to the surroundings, or from the surroundings to the system.

The Quantum-Mechanical Model of an Atom

The Quantum-Mechanical Model of an Atom

Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra.

First Law: Particles in One-dimensional Equilibrium

First Law: Particles in One-dimensional Equilibrium

Newton's first law of motion states that a body at rest remains at rest, or if in motion, remains in motion at constant velocity, unless acted on by a net external force. It also states that there must be a cause for any change in velocity (a change in either magnitude or direction) to occur. This cause is a net external force. For example, consider what happens to an object sliding along a rough horizontal surface. The object quickly grinds to a halt, due to the net force of friction. If...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by

Same author

Entropy Flow at the Quantum Limit.

Nano letters·2026

Same author

Adaptive catalytic compartments emerge from synergistic integration of DNA nanostructures and transient coacervates.

Nanoscale horizons·2025

Same author

Acute elevated blood pressure in the inpatient setting.

Heart (British Cardiac Society)·2025

Same author

Evaluating Radioactive Analogs of Doxorubicin to Quantify ChemoFilter Binding and Whole-Body Positron Emission Tomography/Magnetic Resonance Imaging for Drug Biodistribution.

Journal of vascular and interventional radiology : JVIR·2022

Same author

Morphological and Transcriptional Responses to CRISPRi Knockdown of Essential Genes in Escherichia coli.

mBio·2021

Same author

Emergence of Fourier's Law of Heat Transport in Quantum Electron Systems.

ACS nano·2018

Same journal

Erratum: Bacterial Turbulence at Compressible Fluid Interfaces [Phys. Rev. Lett. 136, 138301 (2026)].

Physical review letters·2026

Same journal

Unveiling Light-Quark Yukawa Flavor Structure via Dihadron Fragmentation at Lepton Colliders.

Physical review letters·2026

Same journal

Adaptable Route to Fast Coherent State Transport via Bang-Bang-Bang Protocols.

Physical review letters·2026

Same journal

Topological Transition and Emergence of Elasticity of Dislocation in Skyrmion Lattice: Beyond Kittel's Magnetic-Polar Analogy.

Physical review letters·2026

Same journal

Pound-Drever-Hall Method for Superconducting-Qubit Readout.

Physical review letters·2026

Same journal

Coupling a ^{73}Ge Nuclear Spin to an Electrostatically Defined Quantum Dot in Silicon.

Physical review letters·2026

See all related articles

Search research articles

Related Experiment Video

Updated: Jun 14, 2025

Measurement of Quantum Interference in a Silicon Ring Resonator Photon Source

Measurement of Quantum Interference in a Silicon Ring Resonator Photon Source

Published on: April 4, 2017

Work Sum Rule for Open Quantum Systems.

Parth Kumar¹, Caleb M Webb¹, Charles A Stafford¹

¹Department of Physics, <a href="https://ror.org/03m2x1q45">University of Arizona</a>, 1118 East Fourth Street, Tucson, Arizona 85721, USA.

Physical Review Letters

|August 30, 2024

Summary

This summary is machine-generated.

We found a unique way to partition thermodynamic quantities in open quantum systems using Hilbert space. This method ensures entropy remains consistent and clarifies how quantum work is distributed, even nonlocally.

More Related Videos

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Isotopic Effect in Double Proton Transfer Process of Porphycene Investigated by Enhanced QM/MM Method

Isotopic Effect in Double Proton Transfer Process of Porphycene Investigated by Enhanced QM/MM Method

Published on: July 19, 2019

Related Experiment Videos

Last Updated: Jun 14, 2025

Measurement of Quantum Interference in a Silicon Ring Resonator Photon Source

Measurement of Quantum Interference in a Silicon Ring Resonator Photon Source

Published on: April 4, 2017

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Isotopic Effect in Double Proton Transfer Process of Porphycene Investigated by Enhanced QM/MM Method

Isotopic Effect in Double Proton Transfer Process of Porphycene Investigated by Enhanced QM/MM Method

Published on: July 19, 2019

Area of Science:

Thermodynamics
Quantum Mechanics
Statistical Physics

Background:

Partitioning thermodynamic quantities in open quantum systems is crucial.
Defining entropy, work, and internal energy consistently between system and environment remains challenging.

Purpose of the Study:

To identify a robust method for partitioning thermodynamic quantities in open quantum systems.
To resolve ambiguities in defining entropy and work in quantum thermodynamics.
To establish path independence for system state functions.

Main Methods:

Hilbert space partitioning for system-environment coupling.
Derivation of a quantum work sum rule.
Analysis of thermodynamic quantities in a driven resonant level model.

Main Results:

Entropy is nonsingular only under a Hilbert space partition (50/50 system-environment coupling).
Quantum work exhibits nontrivial partitioning, requiring a nonlocal work sum rule.
State functions become path independent when nonlocal quantum work is included.

Conclusions:

A Hilbert space partition provides a consistent framework for quantum thermodynamics.
The nonlocal nature of quantum work is essential for defining thermodynamic state functions.
The findings offer a new perspective on energy and entropy flow in quantum systems.